Search NASA⌕ Search

SEARCH · Search NASA

Results for “linear least squares”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

117 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Surface analysis insight note: Illustrating the effect of adventitious contamination on Pt photoemission peak intensities

Adventitious carbon contaminations are not only omnipresent and used for charge referencing of XPS spectra but also can alter the apparent presence of the element peaks that span over the large spectral window of binding energies. This Insight note describes the effect of an adventitious contamination layer on Pt and presents, in brief, the approach whereby the component spectra are derived for ion beam cleaned Pt samples that can then utilize linear mathematics to peak fit said spectra thus quantifying the amount of each component including that assigned to the contamination itself of Pt metal.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Precise Modeling of a Complex Solenoidal Magnetic Field Using a Combination of Analytic Functions and a PINN

We demonstrate an iterative approach to modeling a sparsely measured magnetic field in a large-bore solenoid. This approach uses a hybrid of traditional and machine learning techniques. The traditional technique is a linear least-squares fit using a series solution to Laplace's equation, while the machine learning technique involves the training of a physics-informed neural network (PINN) on the least-squares fit residuals. We use a newly defined activation function "DELTAsnake," a modification to the snake activation function proposed by Ziyin et al. that allows for stronger curvature and non-monotonicity. The combined model approximately obeys Maxwell's equations to a level sufficient for producing high quality physics simulations and analysis. Our approach is applied to a highly realistic calculation of the expected magnetic field in the Mu2e experiment's Detector Solenoid which includes a simple model for the expected statistical measurement uncertainties. Using ten toy measurement simulations, we demonstrate the capabilities of our model in comparison to the least-squares method alone; the least-squares method alone results in a reduced chi-squared statistic of ${2.15 \pm 0.01}$, while our approach improves the reduced chi-square to ${1.034 \pm 0.005}$. Furthermore, for an average toy simulation, we show that the range of the RMS of the three field component residuals reduces from ${0.07-0.37}$ Gauss to ${0.05-0.07}$ Gauss. We find that this novel method is robust against a realistic systematic uncertainty deriving from Hall probe calibration bias and can be used to significantly reduce the number of measurements required to achieve an accurate model.

Kampa, Cole [Caltech] (ORCID:0000000192972920)↗
DOE OSTI2026

Fast Active-Set Thresholding Method for Nonnegative Least Squares

Nonnegative Least Squares (NNLS) is a fundamental constrained optimization problem encountered in many applications such as image deblurring, signal processing, nonnegative matrix factorization, magnetic microscopy, and hyperspectral imaging. Active-set based methods are a common class of algorithms for solving NNLS which identify the optimal variable set of the NNLS solution. They do so by iteratively solving a series of unconstrained least squares problems, identifying which variables violate the nonnegativity constraints, and then swapping variables in/out of consideration until the optimal set of variables is found. Several variations improving upon this method exist in the literature. In this work, we propose an active-set swap heuristic which further improves upon existing active-set based methods for NNLS. Our optimizations are based upon adding multiple variables to the passive set within a threshold of the smallest gradient value and removing variables within a similar threshold of the closest boundary constraint. We leverage these optimizations to yield a Fast Active-Set Thresholding NNLS (FAST-NNLS) algorithm which significantly outperforms the existing state-of-the-art NNLS algorithms for a wide range of problems. Rigorous convergence guarantees are proven for the proposed method. We demonstrate the effectiveness of our proposed method on multiple synthetic datasets and two realworld text analysis applications. In doing so, we present the most comprehensive NNLS solver comparison in the literature to date.

Cobb, Benjamin [Georgia Institute of Technology]↗
DOE OSTI2026

A Tutorial on Bayesian analysis of linear shock compression data

Gas gun and other shock compression experiments often produce shock wave velocity measurements that are linearly associated with particle velocity. Traditionally, this empirical relationship is quantified with a single Hugoniot curve that is estimated using least squares regression. However, for downstream modeling and simulation tasks, it is often more useful to have multiple Hugoniot curves in the pressure–volume plane that are consistent with the data. We employ Bayesian uncertainty quantification methods as a framework for propagating measurement uncertainty through to model parameters and predictions. Specifically, this Tutorial shows how to sample multiple Hugoniot curves in the pressure–volume plane that are consistent with the shock wave-particle velocity measurements in a two-step Bayesian approach. First, we obtain an analytical expression for the posterior distribution of the linear model parameters using Bayesian linear regression. Second, we propagate samples from the posterior distribution through the Rankine–Hugoniot equations to yield Hugoniot curves in the pressure–volume plane. The procedure is demonstrated with publicly available data on argon, copper, and nickel, and compared against bootstrapping and linear regression. The Bayesian procedure is shown to be interpretable, computationally inexpensive, and less sensitive than an alternative bootstrapping approach to the removal of the point in the copper dataset that has the largest particle velocity. As a Tutorial on Bayesian methodology for the shock compression community, we provide several derivations and explanations that make this paper self-contained, and make all code and data available at github.com/llnl/BALSCD.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Geospatial modeling of near subsurface temperatures of the contiguous United States for assessment of materials degradation

Abstract Understanding subsurface temperature variations is crucial for assessing material degradation in underground structures. This study maps subsurface temperatures across the contiguous United States for depths from 50 to 3500 m, comparing linear interpolation, gradient boosting (LightGBM), neural networks, and a novel hybrid approach combining linear interpolation with LightGBM. Results reveal heterogeneous temperature patterns both horizontally and vertically. The hybrid model performed best achieving a root mean square error of 2.61 °C at shallow depths (50–350 m). Model performance generally decreased with depth, highlighting challenges in deep temperature prediction. State-level analyses emphasized the importance of considering local geological factors. This study provides valuable insights for designing efficient underground facilities and infrastructure, underscoring the need for depth-specific and region-specific modeling approaches in subsurface temperature assessment.

Science & Technology - Other Topics↗
DOE OSTI2025

Engineering 2D Square Lattice Hubbard Models in 90° Twisted GeX/SnX (X =S, Se) Moiré Superlattices

Because of the large-period superlattices emerging in moiré two-dimensional (2D) materials, electronic states in such systems exhibit low energy flat bands that can be used to simulate strongly correlated physics in a highly tunable setup. While many investigations have thus far focused on moiré flat bands and emergent correlated electron physics in triangular, honeycomb, and quasi-one-dimensional lattices, tunable moiré realizations of square lattices subject to strong correlations remain elusive. Here, in this work, we propose a feasible scheme to construct moiré square lattice systems by twisting two or more layers of 2D materials in a rectangular lattice by 90°. We demonstrate the concept with twisted GeX/SnX (X =S, Se) moiré superlattices and calculate their electronic structures from first principles. We show that the lowest conduction flat band in these systems can be described by a square lattice Hubbard model with parameters which can be controlled by varying the choice of host materials, number of layers, and external electric fields. In particular, twisted double bilayer GeSe realizes a square lattice Hubbard model with strong frustration due to the next-nearest-neighbor hopping that could host unconventional superconductivity, in close analogy to the Hubbard model for copper-oxygen planes of cuprate high-temperature superconductors. The presented scheme uses 90° twisted 2D materials with rectangular unit cells as a promising platform for realizing the physical phenomena of square lattice Hubbard models, establishing a new route for studying its rich phase diagram of magnetism, charge order, and unconventional superconductivity in a highly tunable setting.

2-dimensional systems↗
DOE OSTI2026

Superconducting phase diagram of multilayer square-planar nickelates

The discovery of superconductivity in square-planar nickelates has offered a rich materials platform to explore the origins of high-temperature superconductivity. However, experimental investigations have largely been limited to the infinite-layer R NiO 2 ( R , rare earth) nickelates. For this work we constructed a phase diagram of multilayer square-planar Nd n+1 Ni n O 2n+2 compounds and found signatures of superconductivity for dimensionality n = 4 to 8. Upon decreasing n , the superconducting anisotropy evolves owing to 4ƒ electron effects, and electronic structure characteristics approach cuprate-like behavior. Magnetic fluctuations persist from within the superconducting regime and into the overdoped, nonsuperconducting regime. The superconducting regime overlaps with that of chemically doped infinite-layer nickelates, demonstrating underlying commonalities as well as differences across varying structural realizations of square-planar nickelates. Our work establishes this layered template for creating new nickel-based superconductors.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Full-core high-burnup BWR LOCA fuel performance analysis and FFRD susceptibility

The susceptibility of the boiling water reactor (BWR) Limerick Unit 1 to fuel fragmentation, relocation, and dispersal during a postulated large-break loss-of-coolant accident (LBLOCA) was calculated using a multiphysics framework. The simulations include full-core, rod-resolved neutronic, thermal hydraulic, and fuel performance models using the VERA, TRACE, and BISON codes. This work focused on the transient BISON simulations, which include both the normal operation and LBLOCA periods in the same simulations. Cladding integrity was assessed using two correlations that are included with BISON. make page break Several new BWR-specific features were recently added to BISON. This work represents the first time these features have been included in a core-scale set of simulations. This study hence evaluates the performance of these new models for an operating reactor with realistic operating conditions. Simulation results showed that cladding integrity was maintained (i.e., no rods burst). Finally, future work to improve BWR and PWR predictions using this framework is suggested.

BISON↗
DOE OSTI2024

Surface science insight note: A linear algebraic approach to elucidate native films on Fe 3 O 4 surface

Standard materials are often used to obtain spectra that can be compared to those from unknown samples. Spectra measured from these known substances are also used as a means of computing sensitivity factors to allow quantification by X-ray photoelectron spectroscopy (XPS) of less well-defined materials. Spectra from known materials also provide line shapes suitable for inclusion in spectral models which, when fitted to spectra, permit the chemical state for a sample to be assessed. Both types of information depend on isolating photoemission signals from the inelastically scattered signal. In this Insight note, technical issues associated with the use of XPS of as received Fe 3 O 4 powder sample surface are discussed. The Insight note is designed to show how linear algebraic techniques applied to data collected from a sample marketed as pure Fe 3 O 4 powder are used to verify that XPS has been performed on chemistry representative of the sample. The methods described in this Insight note can further be utilized in elucidating complex XPS data obtained from thin films formed or evolved during cyclic/non-steady use of complex (electro)catalyst surfaces, especially in the presence of contaminants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Linear Dichroism of the Optical Properties of SnS and SnSe Van der Waals Crystals

Abstract Tin monochalcogenides SnS and SnSe, belonging to a family of Van der Waals crystals isoelectronic to black phosphorus, are known as environmentally friendly materials promising for thermoelectric conversion applications. However, they exhibit other desired functionalities, such as intrinsic linear dichroism of the optical and electronic properties originating from strongly anisotropic orthorhombic crystal structures. This property makes them perfect candidates for polarization‐sensitive photodetectors working in near‐infrared spectral range. A comprehensive study of the SnS and SnSe crystals is presented, performed by means of optical spectroscopy and photoemission spectroscopy, supported by ab initio calculations. The studies reveal the high sensitivity of the optical response of both materials to the incident light polarization, which is interpreted in terms of the electronic band dispersion and orbital composition of the electronic bands, dictating the selection rules. From the photoemission investigation the ionization potential, electron affinity and work function are determined, which are parameters crucial for the design of devices based on semiconductor heterostructures.

Chemistry↗
DOE OSTI2026

Modeling of a Four-Stage Linear Ionization Cooling Channel for a Muon Collider in G4Beamline

A previous study of an eight-stage rectilinear ionization cooling channel in the ICOOL software demonstrated a five-order-of-magnitude reduction in a muon beam’s 6D emittance. In this study, we look to compare the ways ICOOL and Muons, Inc.’s g4Beamline software model ionization cooling by comparing their modeling of the first four stages to this optimized cooling channel constructed in ICOOL. We begin by identifying the parameters used to construct the optimized ionization cooling channel in ICOOL. We then reconstruct this beam in g4Beamline with identical parameter specifications and simulate the cooling of an identical input beam. Finally, we compare the two simulations based on their beam transmission, longitudinal emittance, and transverse emittance along the channel length. Through this process, we demonstrate that G4Beamline accurately reproduces transverse cooling results but predicts systematically different longitudinal emittance evolution while maintaining similar overall cooling performance, reproducing a 97.9% reduction in 6D emittance over four stages.

Keeler, Dominic [Purdue U., West Lafayette] (ORCID↗
DOE OSTI2026

Uncovering the linear boron environment in Na 3 BP 2 through solid-state 11 B NMR spectroscopy

Boron-based compounds exhibit a wide range of structural diversity, with potential applications spanning organic and inorganic chemistry. Herein, we focus on the characterization of the linear boron-phosphorus unit P═B═P in Na 3 BP 2 using solid-state nuclear magnetic resonance (ssNMR) spectroscopy and density functional theory (DFT) calculations. High-resolution 11 B ssNMR spectra were recorded at two fields, and key parameters such as chemical shift anisotropy (CSA), quadrupolar coupling constants (C Q ), and electric field gradient (EFG) tensors were extracted. The 11 B NMR results revealed a distinct chemical environment for the two-coordinate boron atom, with a CSA span (Ω) of 280 ppm and a C Q of 3.0 MHz. These values were further validated through periodic plane-wave DFT calculations, which showed good agreement with experimental results. The obtained spectral parameters are compared to other linear boron units, such as the BO 2 motif, providing a broader context for understanding boron coordination in inorganic compounds. This work expands the body of NMR knowledge on boron-containing materials, particularly for linear boron motifs. The findings contribute to the growing field of boron chemistry and its potential applications in advanced materials.

Porter, Andrew P. [Ames Laboratory (AMES), Ames, I↗
DOE OSTI2025

Mechanically Accelerated Depolymerization of Entangled Linear Polymer Melts

Mechanical forces can enhance the chemical depolymerization of synthetic polymers when shear flow accelerates chain scission. To quantify the extent of mechanically-accelerated scission, the effect of simple shear flow (duration and strength) with low Weissenberg and Deborah numbers was investigated by considering the impact of applied work in both simple shear and shear dominated mixed flows. Hydrogenated polyisoprene was chosen as a model linear, entangled system. The conditions (strain amplitude, frequency, and shearing time) necessary to increase chain scission were assessed in the rubbery melt. Shear flow accelerated chain scission at higher temperatures, suggesting an activated process. Isothermal scission versus work curves were superposed by applying shift factors a T,S , whose Arrhenius-like temperature dependence gave an apparent activation energy for chain scission of ~ 110 kJ/mol, which is likely a combination of the activation energy of viscosity and bond energy. This work provides a base for quantifying the impact of shear on depolymerization of polymer melts and highlight the connection between viscous dissipation and scission chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Echo state network for coarsening dynamics of charge density waves

An echo state network (ESN) is a type of reservoir computer that uses a recurrent neural network with a sparsely connected hidden layer. Compared with other recurrent neural networks, one great advantage of ESN is the simplicity of its training process. Yet, despite the seemingly restricted learnable parameters, ESN has been shown to successfully capture the spatial-temporal dynamics of complex patterns. Here we build an ESN to model the coarsening dynamics of charge-density waves (CDWs) in a semiclassical Holstein model, which exhibits a checkerboard electron density modulation at half-filling stabilized by a commensurate lattice distortion. The inputs to the ESN are local CDW order parameters in a finite neighborhood centered around a given site, while the output is the predicted CDW order of the center site at the next time step. Special care is taken in the design of couplings between hidden layer and input nodes to ensure lattice symmetries are properly incorporated into the ESN model. Since the model predictions depend only on CDW configurations of a finite domain, the ESN is scalable and transferrable in the sense that a model trained on dataset from a small system can be directly applied to dynamical simulations on larger lattices. Furthermore, our work opens avenues for efficient dynamical modeling of pattern formations in functional electron materials.

2-dimensional systems↗
DOE OSTI2024

X-ray linear dichroic tomography of crystallographic and topological defects

Abstract The functionality of materials is determined by their composition 1–4 and microstructure, that is, the distribution and orientation of crystalline grains, grain boundaries and the defects within them 5,6 . Until now, characterization techniques that map the distribution of grains, their orientation and the presence of defects have been limited to surface investigations, to spatial resolutions of a few hundred nanometres or to systems of thickness around 100 nm, thus requiring destructive sample preparation for measurements and preventing the study of system-representative volumes or the investigation of materials under operational conditions 7–15 . Here we present X-ray linear dichroic orientation tomography (XL-DOT), a quantitative, non-invasive technique that allows for an intragranular and intergranular characterization of extended polycrystalline and non-crystalline 16 materials in three dimensions. We present the detailed characterization of a polycrystalline sample of vanadium pentoxide (V 2 O 5 ), a key catalyst in the production of sulfuric acid 17 . We determine the nanoscale composition, microstructure and crystal orientation throughout the polycrystalline sample with 73 nm spatial resolution. We identify and characterize grains, as well as twist, tilt and twin grain boundaries. We further observe the creation and annihilation of topological defects promoted by the presence of volume crystallographic defects. The non-destructive and spectroscopic nature of our method opens the door to operando combined chemical and microstructural investigations 11,18 of functional materials, including energy, mechanical and quantum materials.

Science & Technology - Other Topics↗